A Dark Witch or Wizard is any magical person who primarily studies and/or practices the Dark Arts. They may also possess some dark objects like Horcruxes.
Some of the magic they have been known to practise includes use of the three Unforgivable Curses, creating or brewing dark potions, putting use to/using dark objects, animating Inferi[1], and attracting all kinds of Dark creatures to make huge armies and command them to attack their enemies[2]. Noted Dark wizards and witches include Herpo the Foul, Morgan le Fay, Gellert Grindelwald, and Lord Voldemort, as well as the latter's followers, known as Death Eaters.
Others who might be considered Dark wizards are the owners and customers of shops such as Borgin and Burkes, and arguably students of Durmstrang Institute, as the curriculum there teaches much of the Dark Arts[3]. Many Dark wizards and witches appear to believe in the importance of blood purity and to hate Muggles, though there is not necessarily a connection.
In the Harry Potter films most Dark Wizards appear to Apparate differently than 'white wizards'. Dark ones Disapparate by turning into a whirlwind of black smoke and flying into the air, and then spiralling back down to the desired spot.
Meanwhile, white wizards can just pop and disappear, or similarly can disappear in a whirlwind of white smoke. The ability to conjure this whirlwind may reflect an advanced wizard or witch.
In LEGO Harry Potter: Years 1-4 and its sequel, only Dark Wizards could use magic on the items that had red sparks, symbolising Dark Magic.